Amplitude vs velocity

I have already posted (at school) my answer to this one, but the more I think about it, the more I'm confused.

The question is "When playing a violin, the effect produced when the bow is drawn faster across the string is;
a. A higher pitch.
b. greater wave velocity in the string.
c. a louder sound.
d. all of these.
e. none of these... no discernable effect.

My answer was C. I belive the the faster the bow is drawn across the string will increase the amplitude of the wave thereby increasing it's volume.
B is giving me some difficulty. If the amplitude of the wave/string is increased, would'nt the velocity of the string have to increase in order to have the same Hz with a greater distance Peak to Peak?

And the velocity of the wave is determined by the material of the string. If you have any doubts about this, consider that you can shout faster, harder, higher, lower, whatever, nothing you do will change the speed with which your voice travels through the air at a given temperature and pressure.

So that eliminates a, b and d.

To produce a louder sound, you would have to supply more energy to the string. I don't think moving the bow more quickly across the string supplies MORE energy. It seems to me that the faster bow supplies the same amount of energy, but in a shorter period of time. So, if the velocity and frequency are the same, and the amount of energy is the same, why would the sound be louder? (On the other hand, pressing harder with the bow would transfer more energy, and therefore would produce a louder sound.)

Maybe I am mistaken, I thought that by drawing the bow faster was adding energy to the wave, thereby increasing the amplitude. If the amplitude of the wave is increases does'nt the volume of the sound increase?

I'm still questioning answer b because I read it not to ask if the wave (sound speed) is increased, but if the back and forth velocity of the string itself is increased. Same Hz, same speed of the sound traveling from the string, but the string simply has travel faster if the Peak to Peak distance (amplitude) is increased in the sine wave at the same HZ? It is how they worded the answer that is killing me.

All kidding aside, there is no "other" velocity. The velocity of the wave IS the speed with which the sound travels along the string. I'm not sure what you have in mind when you say the "back and forth" motion of the string. It sounds like you are talking about the linear velocities of the vibrating molecules, but that's just another way of describing the frequency. It's not a third kind of movement.

You're right that increasing the amplitude would increase the volume. You may be correct, but I don't think that moving the bow faster increases the energy. I think that if there is a single stroke of the bow, with a given amount of pressure, the same amount of energy is transferred whether it takes 2 seconds or 1/4 second to complete the stroke.

If it helps any, the mechanism for bow-induced string oscillation is a stick-slip phenomenon, meaning it is largely characterized by static friction between the bow hairs and the surface of the string. The string is carried by the bow until the component of string tension along the bow is greater than the maximum static friction value, at which point string and bow slide relative to each other. It is then "caught" by static friction again and the cycle repeats. The point at which the static friction is reached at every one of these cycles is determined by the geormetry of the configuration (you can assume a constant string tension and resolve into components in a stretched position, or you could include string elasticity if you want to make the model more complicated). The amplitude of the string oscillations should, therefore, be unaffected by the bow speed (but they would be affected by bow pressure --> increased static friction).